Adversary lower bounds for the collision and the set equality problems

Adversary lower bounds for the collision and the set equality problems

We prove tight Ω(n1/3) lower bounds on the quantum query complexity of the Collision and the Set Equality problems, provided that the size of the alphabet is large enough. We do this using the negative-weight adversary method. Thus, we reprove the result by Aaronson and Shi, as well as a more recent...

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Main Authors: Belovs, Aleksandrs, Rosmanis, Ansis
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2020
Subjects:
Science::Physics
Quantum Physics
Set Equality
Online Access:https://hdl.handle.net/10356/137663
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1376632023-02-28T19:51:02Z Adversary lower bounds for the collision and the set equality problems Belovs, Aleksandrs Rosmanis, Ansis School of Physical and Mathematical Sciences Centre for Quantum Technologies Science::Physics Quantum Physics Set Equality We prove tight Ω(n1/3) lower bounds on the quantum query complexity of the Collision and the Set Equality problems, provided that the size of the alphabet is large enough. We do this using the negative-weight adversary method. Thus, we reprove the result by Aaronson and Shi, as well as a more recent development by Zhandry. NRF (Natl Research Foundation, S’pore) Published version 2020-04-08T02:34:15Z 2020-04-08T02:34:15Z 2017 Journal Article Belovs, A., & Rosmanis, A. (2017). Adversary lower bounds for the collision and the set equality problems. Quantum Information and Computation, 18(3-4). 1533-7146 https://hdl.handle.net/10356/137663 arXiv:1310.5185 3-4 18 en Quantum Information and Computation © 2017 Rinton Press. All rights reserved. This paper was published in Quantum Information and Computation and is made available with permission of Rinton Press. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Physics
Quantum Physics
Set Equality
spellingShingle Science::Physics
Quantum Physics
Set Equality
Belovs, Aleksandrs
Rosmanis, Ansis
Adversary lower bounds for the collision and the set equality problems
description We prove tight Ω(n1/3) lower bounds on the quantum query complexity of the Collision and the Set Equality problems, provided that the size of the alphabet is large enough. We do this using the negative-weight adversary method. Thus, we reprove the result by Aaronson and Shi, as well as a more recent development by Zhandry.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Belovs, Aleksandrs
Rosmanis, Ansis
format Article
author Belovs, Aleksandrs
Rosmanis, Ansis
author_sort Belovs, Aleksandrs
title Adversary lower bounds for the collision and the set equality problems
title_short Adversary lower bounds for the collision and the set equality problems
title_full Adversary lower bounds for the collision and the set equality problems
title_fullStr Adversary lower bounds for the collision and the set equality problems
title_full_unstemmed Adversary lower bounds for the collision and the set equality problems
title_sort adversary lower bounds for the collision and the set equality problems
publishDate 2020
url https://hdl.handle.net/10356/137663
_version_ 1759856186521288704

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